Liz is getting married, and she wants to have her wedding reception at an event center. The event center uses a function of the form C(x)=mx+b, where m and b are constants, to determine the cost of a wedding reception with x guests. This table shows two values of the function.
x C(x)
20 390
30 510
Find an expression for C(x). Write your answer in the form C(x)=mx+b, where m and b are integers or decimals. Do not round.
To find the expression for C(x), we need to find the values of m and b in the function C(x)=mx+b.
First, we can use the two given points (20, 390) and (30, 510) to set up a system of equations.
Using the point (20, 390):
390 = 20m + b
Using the point (30, 510):
510 = 30m + b
Now, we can solve this system of equations. Subtracting the first equation from the second one, we get:
510 - 390 = 30m + b - (20m + b)
120 = 10m
m = 12
Now that we know the value of m, we can substitute it back into one of the equations to solve for b. Using the equation 390 = 20m + b:
390 = 20(12) + b
390 = 240 + b
b = 150
Therefore, the expression for C(x) is:
C(x) = 12x + 150